- You are here:
- GT Home
- Home
- News & Events

Series: Research Horizons Seminar

If Google Scholar gives you everything you want, what could Georgia Tech Library possibly do for you? Come learn how to better leverage the tools you know and discover some resources you may not. Get to know your tireless Math Librarian and figure out how to navigate the changes coming with Library Next. This is also an opportunity to have a voice in the Library’s future, so bring ideas for discussion.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

We present a multiscale approach for identifying objects submerged in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial, and military applications. The forward model incorporates simulations, by solving Helmholtz equations, on a wide range of spatial scales in the seafloor geometry. This allows for detailed recovery of seafloor parameters including the material type. Simulated backscattered data is generated using microlocal analysis techniques. In order to lower the computational cost of large-scale simulations, we take advantage of a library of representative acoustic responses from various seafloor parametrizations.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

A knot is a smooth embedding of S^1 into S^3 or R^3. There is a natural way to "add" two knots, called the connected sum. Under this operation, the set of knots forms a monoid. We will quotient by an equivalence relation called concordance to obtain a group, and discuss what is known about the structure of this group.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

A fundamental result in Harmonic Analysis states that many functions defined over the interval [-\pi,\pi] can be decomposed into a Fourier series, that is, decomposed as sums of sines and cosines with integer frequencies. This allows one to describe very complicated functions in a simple way, and therefore provides with a strong tool to study the properties of different families of functions.However, the above decomposition does not hold -- or holds but is not efficient enough-- if the functions are no longer defined over an interval,( e.g. if a function is defined over a union of two disjoint intervals). We will discuss the question of whether similar decompositions are possible also in such cases, with the frequencies of the sines and cosines possibly being no longer integers.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

Many conservative PDE models can be written in a Hamiltonian form. They include Euler equations in fluids, Vlasov models for plasmas and galaxies, ideal MHD for plasmas, Gross–Pitaevskii equation for superfluids and Bose-Einstein condensates, and various water wave models (KDV, BBM, KP, Boussinesq systems etc). I will describe some dynamical problems of these models, from a more unifying point of view by using their Hamiltonian forms. They include: stability/instability of coherent states (steady solution, traveling waves, standing waves etc.), invariant manifolds near unstable states, and inviscid and enhanced damping in fluids and plasmas. It is a topic course that will be taught in the fall.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

Abstract: Certain materials form geometric structures called "grains," which means that one has distinct volumes filled with the same semi-solid material but not mixing. This can happen with semi-molten copper and something like this can also happen with liquid crystals (which are used in some calculator display screens). People who try to analyze such systems tend to be interested in the motion of the boundaries between grains (which are often modeled by mean curvature flow) and the motions of the exterior surfaces of grains (which are often modeled by surface diffusion flow). Surfaces of constant mean curvature are stationary for both flows and provide stationary or equilibrium configurations. The surfaces of constant mean curvature which are axially symmetric have been classified. Grain boundaries are not usually axially symmetric, but I will describe a model situation in which they are and one can study the resulting equilibria. I will give a very informal introduction to the flow problems mentioned above (about which I know very little) and then go over the classification of axially symmetric constant mean curvature surfaces (about which I know rather more) and some reasonable questions one can ask (and hopefully answer) about such problems.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

Compressive sensing is a (relatively) new paradigm in data analysis that is having a large impact on areas from signal processing, statistics, to scientific computing. I am teaching a special topics on the subject in the Fall term, in support of the GT-IMPACT program. The talk will list some basic principles in the subject, stating some Theorems, and using images, and sounds to illustrate these principles.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

Abstract: If P(z) is a polynomial, then log|P(z)| is a potential. We discuss some facets of this observation, and some gems in classical potential theory. A special topics course on potential theory will be offered in the fall.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

We shall introduce and discuss several notions from classical Convex geometry. In particular, covering number, separation number and illumination number shall be defined and explored. Another parameter, which has been studied in the recent years, the dilated covering number of a convex set shall be introduced. We shall present best known estimate on this number, which is a part of a joint work with K. Tikhomirov.

Series: Research Horizons Seminar

Food and Drinks will be provided before the seminar.

Abstract: It is not necessary to know what étale, motivic, or homotopy mean for this talk. The talk is intended to advertise motivic homotopy theory, and introduce it a little too. To do this, we'll give an example of an elementary problem the field can be used to solve, and then describe some aspects of the field itself which make this possible. The part of this talk which is original is joint with Jesse Kass.